I know we were already having this discussion (unresolved) elsewhere, but I will say this:
Of course you can valet park for your ADR. Of course you can valet park for other reasons at the resort as well.
Anecdotal evidence says you can even valet park at a resort and walk to the park because the valet staff do not seem to care. However, that is always at the discretion of the valet staff. Now they of course want tips, so most often they are going to tell you that it's not a problem. The other reason may be because they have a separate valet lot and they are in charge of parking the cars there, so it is up to them to determine who can and can't stay. But there have been a few (very few) reports here that someone received a 3 hour parking pass at the valet stand during peak crowd / holiday times, especially at the resorts that are within walking distance to a park.
Keep in mind that the more turns they get in the valet lot, the more money the company (which is not Disney) makes and the more tips the valet staff make. So when it's very crowded and parking is limited and opportunities for new customers are high -- like @ the Boardwalk, they may limit you even in the valet lots.
People who can self park with an ADR or as guests of that resort still use the valet service - my family does it sometimes. Sometimes we just feel like it, sometimes it's raining, and sometimes we might be walking in the International Gateway after our dinner at the Beach Club. Sometimes I pay $12 to valet park just because I'm on vacation. But valet parking @ the resorts is NOT intended for people to park for theme park access, which seems to be your idea of the only logical reason people would use valet parking since you have to pay for it. Shockingly wasteful, I have left my car in the Poly valet lot for close to a week one time and paid for it every night.
And in our prior conversation, I wasn't questioning parking for dinner, then walking into the park at all. I was being skeptical about whether it was "right" (so subjective) to valet park at a resort in the morning to go to a park, return and get your car, come back later to the same valet lot, have dinner and go back to the park. It was the morning / no ADR part that struck me as kind of hinky for lack of a better word. I'm sure others may have no problem with that.